THE ASTROPHYSICAL JOURNAL, 514:909È931, 1999 April 1 ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A. WIND INHOMOGENEITIES IN WOLF-RAYET STARS. II. INVESTIGATION OF EMISSION-LINE PROFILE VARIATIONS SE BASTIEN LE PINE1 AND ANTHONY F. J. MOFFAT2 De partementde Physique, Universite deMontre al, and Observatoire du Mont-Me gantic, C.P. 6128, Succ. Centre-Ville, Montre al, QC, CANADA H3C 3J7; lepine=astro.umontreal.ca, mo†at=astro.umontreal.ca Received 1997 September 9; accepted 1998 August 4 ABSTRACT We present high-resolution spectroscopic monitoring of the line-proÐle variations (LPVs) in the He II j5411 emission line of four Wolf-Rayet (WR) stars of the WN sequence (HD 96548, HD 191765, HD 192163, and HD 193077) and in the C III j5696 emission line of Ðve WR stars of the WC sequence (HD 164270, HD 165763, HD 192103, HD 192641, and HD 193793). The LPVs are shown to present system- atic patterns: they all consist of a number of relatively narrow emission subpeaks that tend to move from the line centers toward the line edges. We introduce a phenomenological model that depicts WR winds as being made up of a large number of randomly distributed, radially propagating, discrete wind emission elements (DWEEs). This working model is used to simulate LPV patterns in emission lines from a clumped wind. General properties of the LPV patterns are analyzed with the help of novel numerical tools (based on multiscale, wavelet analysis), and simulations are compared to the data. We investigate the e†ects on the LPVs of local velocity gradients, optical depths, various numbers of discrete wind elements, and a statistical distribution in the line Ñux from individual elements. We also investigate how the LPV patterns are a†ected by the velocity structure of the wind and by the extension of the line-emission region (LER). Eight of the stars in our sample are shown to possess strong similarities in their LPV patterns, which can all be explained in terms of our simple model of local wind inhomoge- neities. We Ðnd, however, that a very large number(Z104) of DWEEs must be used to account for the ~1 LPV. Large velocity dispersions must occur within DWEEs, which give rise to thepm D 100 km s line-of-sight velocity dispersions. We Ðnd evidence for anisotropy in the velocity dispersion within DWEEs withpvr D 4pvh, wherepvr andpvh are the velocity dispersions in the radial and azimuthal direc- tions, respectively. We Ðnd marginal evidence for optical depth e†ects within inhomogeneous features, with the escape probability being slightly smaller in the radial direction. The kinematics of the variable features reveals lower than expected radial accelerations, with20 \bR (R ) \ 80, where b andR are \ [ ~1 b * _ * parameters of the commonly used velocity lawv(r) v=(1 R r ) , withv= the terminal wind veloc- ity. The mean duration of subpeak events, interpreted as the crossing* time of DWEEs through the LER, is found to be consistent with a relatively thin LER. As a consequence, the large emission-line broaden- ing cannot be accounted for by the systematic radial velocity gradient from the accelerating wind. Rather, emission-line broadening must be dominated by the large ““ turbulent ÏÏ velocity dispersion pvr suggested by the LPV patterns. The remaining WR star in our sample (HD 191765) is shown to present signiÐcant di†erences from the others in its LPV pattern. In particular, the associated mean velocity ~1 ~1 dispersion is found to be especially large(pm D 350 km s , compared topm D 100 km s in other stars). Accordingly, the LPV patterns in HD 191765 cannot be satisfactorily accounted for with our model, requiring a di†erent origin. Subject headings: instabilities È line: proÐles È stars: mass loss È stars: Wolf-Rayet È turbulence 1. INTRODUCTION that emission lines from di†erent atomic transitions are formed at di†erent depths in the wind. The spectra of Wolf-Rayet (WR) stars are dominated by Current models of WR atmospheres rely on a set of sim- broad emission lines of Helium, with lines of nitrogen in plifying assumptions within the framework of the so-called stars of the WN sequence, or carbon and oxygen in stars of ““ standard model ÏÏ (see, e.g., Hillier 1995; Hamann 1995, the WC/WO sequence. These lines are sometimes accompa- and references therein), which describes the formation of nied by blueshifted P Cygni absorption features. The gener- emission lines in a dense wind photoionized by a hot core. ally accepted interpretation is that the lines are formed in In the standard model, it is assumed that the wind is spher- extended regions of a fast (D103 km s~1), dense (D10~5 ~1 ically symmetric, homogeneous, and stationary. Radiative M_ yr ) stellar wind (see, e.g., Willis 1991). The spectral and statistical equilibrium are adopted, and a monotonic analysis of WR stars is made difficult by the fact that the wind velocity law is Ðxed a priori. These assumptions have usual assumptions of local thermodynamic equilibrium and been used to perform spectral analyses of WR spectra and plane-parallel atmospheres do not apply. Moreover, WR to predict e†ective temperatures and luminosities. However, winds are believed to be stratiÐed in ionization (see, e.g., several systematic deÐciencies have been observed (see, e.g., Schulte-Ladbeck, Eeenens, & Davis 1995), which means Howarth & Schmutz 1992; Hamann, Wessolowski, & Koesterke 1994; Hillier 1996; Schmutz 1997), suggesting 1 Present address: Space Telescope Science Institute, 3700 San Martin that at least some assumptions in the standard model are Drive, Baltimore, MD 21218; lepine=stsci.edu. invalid. 2 Killam Research Fellow of the Canada Council for the Arts. The picture of a smooth, homogeneous wind in WR stars 909 910 LEŠ PINE & MOFFAT Vol. 514 is being challenged by several lines of observational evi- e.g., in HD 191765 (Vreux et al. 1992; McCandliss et al. dence (see Mo†at 1996). Since it is believed that inhomoge- 1994) and in EZ CMa (Robert et al. 1992; St-Louis et al. neous winds might lead to a downward revision of the 1995; Morel, St-Louis, & Marchenko 1997). It is suspected mass-loss rate (Mo†at & Robert 1994), this would have that these periodic variations are linked either to the pres- important implications for evolutionary models of massive ence of a compact companion or to the rotation of global stars (Maeder 1991). Recently, some attempts have been wind structures. However, whereas such a periodic behavior made to relax certain assumptions of the standard model is observed in only a few stars, stochastic variations seem to (Hillier 1996, and references therein), and spectral analysis be present in every WR star observed so far. using clumped wind models has been attempted (Schmutz A phenomenological model has been suggested to explain 1997; Hillier & Miller 1998). the LPV patterns in terms of local overdensities (termed The difficulty in establishing realistic, inhomogeneous ““ blobs ÏÏ or ““ clumps ÏÏ) in WR winds, as being related, e.g., wind models is that clues about the degree of clumping have to compressible, supersonic turbulence (Robert 1992; mainly come from indirect observational methods. For Mo†at et al. 1994). Each clump presumably follows the example, continuum-emission excess in the infrared and general wind expansion, giving rise to one emission-line radio, which is interpreted as excess free-free emission due subpeak as it moves in, through, and out of the LER. A to wind overdensities (Lamers & Waters 1984), was similar inhomogeneous wind model had previously been observed in 18 early-type stars (Runacres & Blomme 1996). investigated (see Antokhin et al. 1992) in relation to devi- Though models of inhomogeneous winds were shown to ations in the shape of an emission-line proÐle for a clumped reproduce the IR and radio excess well (Blomme & wind. A review of the simultaneous photometric, spectro- Runacres 1997), only limited constraints on the detailed scopic, and polarimetric variations expected from such a density structure could be obtained, since observations clumped wind model has been presented elsewhere (Brown mostly depend on the global e†ects of clumping. Stochastic et al. 1995). variations in polarization and photometry of single WR In the Ðrst paper of this series(Le pine, Mo†at, & Henrik- stars were also interpreted in terms of residuals from a sen 1996, hereafter Paper I) we performed a preliminary clumped wind (Robert et al. 1989). Other examples include analysis of LPVs in emission lines of WR stars using the measures in the intensity of the electron-scattering wings in clumped-wind hypothesis as a working model. We investi- some WR emission lines (Hillier 1991), the relative intensity gated the e†ects on the LPV patterns of a hierarchy of of the IR lines of He I and He II (Nugis & Niedzielski 1995), inhomogeneous elements, which might result from the pres- and j-dependence in the secondary eclipse in V444 Cyg ence of self-structured chaos (e.g., compressible turbulence) (Cherepashchuk, Khaliullin, & Eaton 1984). in the wind (Robert 1994; Henriksen 1994). This involved a Although we can directly observe details in the clumpy study of the LPVs in a static situation (i.e., snapshots of the structure of wind-blown bubbles around Wolf-Rayet stars emission line). (see Marston 1997), we cannot yet directly resolve regions In this second paper, we investigate the LPV patterns in a close to the star, where emission lines are formed and the more general way, in terms of a complete, phenomenologi- wind is presumably driven by the intense radiation Ðeld. In cal model of radially propagating, discrete wind elements. the near future, it might be possible to resolve this wind We Ðrst present a database that comprises sets of high- region in c2 Vel, the closest WR star at D250 pc (van der resolution spectra of optical emission lines from nine WR Hucht et al.